Applications of Artificial Intelligence for Organic Chemistry: The DENDRAL Project

ion planning It may be possible to take a coarser view of the problem space, as though we could back off and see the general features while omitting the details. This is one form of planning (a different form than embodied in Heuristic DENDRAL, to be described shortly). We will call it abstraction to keep the terminology clear. In the terms of our paradigm of problem solving, abstraction can be achieved by defining a new set of problem-state descriptions, based on a language that is an abstrac34 APPLICATIONS OF ARTIFICIAL INTELLIGENCE FOR ORGANIC CHEMISTRY tion of the basic language in the sense that one problem-state description in the abstraction language corresponds to many problem-state descriptions in the basic language. The new view of the problem space now offers a diminished set of states and therefore reduces the complexity of the problem. Transformations for the abstraction language defme the connectivity of the abstracted space. If the problem solver can discover a path from initial state to goal state in the abstracted space, he has not solved the original problem but has established a plan. Each step of the plan then becomes a problem in the original space, but the combined complexity of all these problems may be less than the complexity of the original problem. Working backward For some problems the number of alternatives to be searched is fewer if we begin at the goal state and, running the transformations in reverse as it were, search for the initial state. This situation might be the case if there is only one goal state but a multitude of initial states. Working backward is a time-honored procedure in mathematics and logic. Of course it is of no use for problems in which the transformations are not reversible, or when the definition of goal state is in terms to which the transformations cannot apply, as with chess. One would be hard put to play chess by working backward from a definition of checkmate, looking for the initial board configuration. 3.2.2.2 Heuristic generation Generate and test If there is a procedure that can generate candidate solution, goal states in our present terminology, it may be possible to solve problems by the sequential enumeration and checking of potential solutions. This method is frequently called generate and test. Note that in this paradigm it is not the states of the problem space that are generated. Indeed there need not be a problem space of the sort we have been discussing. Here we need only a space of solutions that can be generated for consideration. This paradigm is thus fundamentally different from searching the space of problem states (state-space search). Analogs of the heuristic search methods described above apply to heuristic generation. Statistical information concerning the distribution of solutions (perhaps by categories defined in a “secondary solution description language”) may be used to guide generation, If some measure of goodness is computable from a proposed solution, then a hill-climbing procedure could be used to determine ways of modifying one proposal in appropriate ways. Similarly, if an abstracted description of, the set of solutions can be constructed, it may be possible to search first for the’correct solution class, and then search within that class. These methods do not exhaust the possibilities, but they provide enough structure for our discussion. 3.2.3 Multiple Sources of Knowledge Much more problem-solving power can be achieved if there is more than one source of information that can be used. For this reason purely syntactic problem solvers are inherently less powerful than those that employ semantic information as well. The secret ARTIFICIAL INTELLIGENCE 35 is not that semantic information is more important, but that two sources of guidance are better than one. Jigsaw puzzles are an appropriate image to make this procedure clear. The problem of finding the one arrangement of all the pieces that yields the desired picture may be a very difficult and large combinatorial task. If the puzzle were done with the pieces face down, analogous to having only the “syntactic” information of piece contours, the true difficulty of the problem would become apparent. If all the pieces were of the same shape, squares or hexagons, the problem could only be solved from the “semantic” information of colors and pictured objects and would also be very difficult. Jigsaw puzzles are tractable because both these sources of information are available and can be played off against one another. In terms of the paradigm of state-space search, different sources of information correspond to different problem-state languages. Several of the search heuristics defmed above rely on these secondary languages. Hill climbing needs a language in which to define its gradient of “warmth,” and statistically guided search is based on a rather general but blurry-visioned search for descriptors that have some correlational information. Abstraction planning is another way of bringing to bear different views of the problem space. On a more general level, apart from any of these methods, is the representation problem. A problem has in general many possible representations. It may be possible to choose two or more (rather than just one) in such a way that progress in one statespace search can be transferred to another. Thus those transitions that are difficult in one representation may be bypassed by using a second and vice versa. In the context of heuristic generation, multiple sources of knowledge have the effect of limiting generation to the intersection of the solution sets delimited by each source.